By “crimping” there is understood the production of a non-detachable electrical and mechanical connection (crimp connection) by plastic deformation between a conductor and a crimp contact. Crimping devices are frequently a component of cable preparation devices for preparation of electric cables, in which the cable is cut to length and stripped and in which a crimp contact is then mounted on the stripped conductor end of the cable by a crimping press. The known crimping devices include cable grippers by which the cable ends are fed to the crimping press. As soon as the cable gripper has reached the final axial position over the crimp contact it remains in unchanged axial position until the conclusion of the crimping process and is lowered with use of, in a given case, a lowering device connected with the press member of the crimping press. Crimping devices of that kind have become known from, for example, EP 1 447 888 A1. The known crimping devices have proved satisfactory in practice for conventional cables containing conductors or wires of copper. For reasons of cost and weight, for some time electrical cables with conductors of aluminum have enjoyed increasing popularity. Particularly in the case of the last-mentioned cables, problems can arise during crimping by conventional methods and devices. Thus, during crimping of cables with conductors or wires of aluminum it can happen that the wire material is strongly deformed in the direction of the cable axis in such a way that kinking of the cable between crimp location and cable gripper occurs. This undesired length extension of the cable can cause permanent deformation of the cable.